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Theorems · Theorem · measure theory

MeasureTheory.Measure.singularPart_of_not_haveLebesgueDecomposition

∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α},
  ¬μ.HaveLebesgueDecomposition ν → μ.singularPart ν = 0
Defined in
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue
Cited by
1 results in Mathlib
Foundations
Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
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MeasureTheory.Measure.mutuallySingular_singularPart · cited by 27Measure.mutuallySingular_…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Measure.HaveLebesgueDecomposition · cited by 92Measure.HaveLebesgueDecom…MeasureTheory.Measure.singularPart · cited by 71Measure.singularPartMeasureTheory.Measure.singularPart_def · cited by 5Measure.singularPart_defMeasure.singularPart_of_not_h…CITED BYCITES

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